Mr Key did, however, have some high-level support for his quest from London's Mayor, Boris Johnson, whom Mr Key also met after seeing Mr Cameron.

After that meeting, Mr Johnson said he supported free labour exchanges between the UK, Australia and New Zealand.

Mr Johnson said he believed the United Kingdom should enter a bilateral arrangement to allow New Zealanders and Australians to work in the UK more freely, and vice versa.

"There's no reason in principle why that shouldn't be accomplished. I do think it is a bit of an oddity that we have this unbelievably close relationship with New Zealand, we have a huge New Zealand population in London, but as far as I understand it is quite difficult sometimes for New Zealanders who want to work here to stay on and contribute in the way they might.

"By contrast, you can come from France, Croatia, Slovenia or 28 EU countries without any hindrance whatsoever."

He said the difficulty was that immigration was a very sensitive issue.

"There might be a bit of uphill work to get this onto the statute book, but I think it's worth a go."

Mr Key said New Zealand's priority would now be ensuring that the remaining travel and work rights were not diluted further - including the working holidays 'youth mobility' scheme and ancestry visas for those with British grandparents.

"It's a very tricky situation for [Prime Minister Cameron]. At the end of the day, immigration is a big issue here. With their position with Europe they have enormous numbers of people who can freely and as of right come to the UK and that is putting stress on their system. So we have to acknowledge that."

The restrictions, put in place in 2010, mean skilled New Zealanders must have a job lined up in the UK to secure a visa, rather than get a visa to move there to look for work.

That has meant the number of skilled migrants going to the UK has almost halved and Mr Key has described restrictions as "grossly unfair".

Mr Key said the changes meant it was almost impossible for someone to get a job in the UK from overseas, because UK employers are also required to prove that they cannot recruit someone in the UK itself and the wider EU first. However, he acknowledged changes in New Zealand's favour were unlikely because of the influx from the EU.

Mr Key said other than the immigration niggles and a hefty $190 departure tax on passengers to New Zealand which he said was driving down tourist numbers, the relationship with Britain was strong.

A FREE TRADE DEAL WITH THE EU?

Mr Key also pushed New Zealand's case to begin free trade talks with the EU with Mr Cameron. New Zealand is one of only about five trading countries which has not begun trade talks with the EU, partly because the EU has been bogged down in negotiations with others.

Mr Key said the United Kingdom could help break that stalling pattern as it was an economically powerful member of the EU.

Although Mr Cameron plans to hold a referendum on Britain's part in the EU soon, Mr Key said that his support for free trade talks would still carry some weight.

"They are an important member of the EU and any help they can give us to advance that would be really useful."

He would also raise it with French President Francois Hollande whom he is due to meet next week.

Mr Key and Mr Cameron also discussed New Zealand's bid for a Security Council seat in 2015 and Mr Key said he was hopeful of the UK's backing, although as a permanent member it was unlikely to publicly state it.

The pair also spoke about the centenary of the start of World War I for which numerous commemorations are planned - it was the first issue Mr Cameron raised, including New Zealand's part in Gallipoli, as the pair chatted before the closed-doors meeting began.

Mr Key said later that the war had helped forge the modern relationship with the United Kingdom.

"That is not something we take for granted."

SYRIA TALK

After talks with Mr Cameron and British Foreign secretary William Hague, Mr Key said New Zealand might offer up any expertise it had dealing with chemical weapons if things progressed in Syria.

"In the end it will be a solution the UN will be involved in and New Zealand might, if requested, add support. Anything that can make sure that the people of Syria are never subjected to chemical warfare again is really important."

He said there were high hopes that the Russia solution for Syria would come to fruition and Syria would give up its chemical weapons to the international community. "That would be a tremendous step for the people of Syria. We acknowledge the challenges in having that achieved, but it is a very sensible step forward."

He said there was naturally some scepticism about Syria's response. "But what are the other alternatives? None of them are terribly attractive."